A few questions about psc_id numbers:
Are psc_id numbers unique or are they only unique in combination with a company numbers?
Does a natural person have the same psc_id number for all companies for whom they are the person of significant control?
Can you retrieve a list of companies for which a person or company with a given psc_id is the person of significant control via the API?

So in the PSC snapshot data set, the part:"links": { "self": "/company/09145694/persons-with-significant-control/individual/bIhuKnMFctSnjrDjUG8n3NgOrlU" },

... I'd expect the link /company/09145694/persons-with-significant-control/individual/bIhuKnMFctSnjrDjUG8n3NgOrlU to be unique and the ID bIhuKnMFctSnjrDjUG8n3NgOrlU wouldn't refer to the same entity even if you did find it occuring in another company.